We derive the effective charge- and current-density operators for the strong-coupling limit of a single-band Mott insulator in the presence of spin-orbit coupling and show that the spin-orbit contribution to the effective charge density leads to novel mechanisms for multiferroic behavior. In some sense, these mechanisms are the electronic counterpart of the ionic-based mechanisms, which have been proposed for explaining the electric polarization induced by spiral spin orderings. In addition, the new electronic mechanisms are illustrated by considering cycloidal and proper-screw magnetic orderings on sawtooth and kagome lattices. As for the isotropic case, geometric frustration is crucial for achieving this purely electronic coupling between spin and charge degrees of freedom.